Calling a setting "post-apocalyptic" because there's a previous civilization somewhere in the past doesn't make much sense. Practically every setting would be post-apocalyptic. Is a historical novel set around the time of the American Revolution post-apocalyptic? After all, there have been several long-dead civilizations by the time of the Revolution, plus one of them, Rome, not only collapsed catastrophically (sort of,) but it's actually held up as a model during the Revolution by the prominent political thinkers.

What makes something post-apocalyptic is the lack of a viable replacement for what is lost, plus the fact that the collapse has happened fairly recently. If there isn't at least one person alive who can remember "the Before Time", it's not post-apocalyptic. The post-apoc genre is about that feeling of loss and the despair over what to do next.